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3 years ago

To obtain the area of a sector, what fraction is multiplied by the area of a circle (A = πr2)?

1 answer:

6 0

Let r be a radius of a given circle and α be an angle, that corresponds to a sector.

The circle area is $A=\pi r^2$ and denote the sector area as $A_1$ .
Then $\dfrac{A_1}{A}= \dfrac{\alpha}{2\pi}$ (the ratio between area is the same as the ratio between coresponding angles).

$A_1=\dfrac{\alpha}{2\pi} \cdot A=\dfrac{\alpha}{2\pi} \cdot \pi r^2= \dfrac{r^2\alpha}{2}$ .

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Find the greatest common factor of 9 and 14

Ratling [72]

The biggest common factor number is the GCF number. So the greatest common factor 9 and 14 is 1.

5 0

3 years ago

Read 2 more answers

You purchased concentrated cleaner that must be diluted (watered down)

abruzzese [7]

Answer:

The volume of the concentrated 80 gallons mixture is 20 gallons

The volume of water in the 80 gallons mixture is 60 gallons

Step-by-step explanation:

The given parameters are;

The content of Container A = The cleaner

The concentration of the cleaner = 20% solution

The content of Container B = Pure water

The concentration of the desired solution = 5%

The volume of the required solution = 80 gallons

Let x represent the volume of the concentrated solution and y represent the volume of water in the 80 gallons mixture

Therefore, we have;

20/100 × x + y×0 = 5/100×80

x + y = 80

y = 80 - x

20/100 × x + (80 - x)×0 = 5/100×80

0.2·x = 4

x = 4/0.2 = 20

x = 20 gallons

y = 80 - x = 80 - 20 = 60

y = 60 gallons

The volume of the concentrated solution (80 gallons mixture) = x = 20 gallons

The volume of water in the 80 gallons mixture = y = 60 gallons.

8 0

3 years ago

Assume that women's heights are normally distributed with a mean given by mu equals 61.4 in, and a standard deviation given by

GuDViN [60]

I think that the correct answer is A

3 0

3 years ago

I really need an answer pls I used all my points :’(

Mazyrski [523]

Answer:

266 tickets

Step-by-step explanation:

Ratio of adult tickets to child tickets is 4 : 3

So, if we think of these as "parts", there are 4 parts adult tickets and 3 parts child tickets.

In total there is:

4 + 3 = 7 parts

Now, given 152 adult tickets. If there are 4 parts of adult tickets, how much is each part worth?

152/4 = 38

Total amount of tickets is 7 of these "parts", so total number of tickets is:

38 * 7 = 266 tickets

5 0

3 years ago

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If 30,000 cm2 of material is available to make a box with a square base and an open top, what is the largest possible volume (in

Cloud [144]

Answer:

The largest possible volume of the box is 2000000 cubic meters.

Step-by-step explanation:

The volume ( $V$ ), in cubic centimeters, and surface area ( $A_{s}$ ), in square centimeters, of the box with a square base are described below:

$A_{s} = l^{2}+h\cdot l$ (1)

$V = l^{2}\cdot h$ (2)

Where:

$l$ - Side length of the base, in centimeters.

$h$ - Height of the box, in centimeters.

By (2), we clear $h$ within the formula:

$h = \frac{V}{l^{2}}$

And we apply in (1) and simplify the resulting expression:

$A_{s} = l^{2}+ \frac{V}{l}$

$A_{s}\cdot l = l^{3}+V$

$V = A_{s}\cdot l -l^{3}$ (3)

Then, we find the first and second derivatives of this expression:

$V' = A_{s}-3\cdot l^{2}$ (4)

$V'' = -6\cdot l$ (5)

If $V' = 0$ and $A_{s} = 30000\,cm^{2}$ , then we find the critical value of the side length of the base is:

$30000-3\cdot l^{2} = 0$

$3\cdot l^{2} = 30000$

$l = 100\,cm$

Then, we evaluate this result in the expression of the second derivative:

$V'' = -600$

By Second Derivative Test, we conclude that critical value leads to an absolute maximum. The maximum possible volume of the box is:

$V = 30000\cdot l - l^{3}$

$V = 2000000\,cm^{3}$

The largest possible volume of the box is 2000000 cubic meters.

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3 years ago